THERMODYNAMICS...Steady flow process Mass balance Energy Balance Steady flow energy equation Nonflow...

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2 Career Avenues GATE Coaching by IITians

THERMODYNAMICS

CONTENTS

1 BASIC CONCEPTS

IN THERMODYNAMICS

Thermodynamic system, surroundings, universe,

system boundary

Types of thermodynamic system

Macroscopic and microscopic point view

Properties of system

Intensive and Extensive properties

State of system

Thermodynamic process, path and cycle

Thermodynamic equilibrium

Quasi-static process

Concept of continuum

Point function and path function

Working substance

Pressure

Mass Density

Weight Density

Specific volume

Specific gravity

Solved Examples

2 TEMPERATURE

Zeroth law of thermodynamics

Thermometric property

Electrical resistance thermometer

Thermocouple

Ideal gas thermometers

Constant volume gas thermometers

Constant pressure gas thermometers

Temperature scales

Thermodynamic temperature scales

Ideal gas

Ideal gas temperature

International Practical temperature scales

Solved Example

3 WORK AND HEAT TRANSFER

Energy transfer by work

Energy transfer by heat

Indicator diagram

Free expansion

Solved Example


4 FIRST LAW OF

THERMODYNAMICS

Joule’s equivalent of heat

First law for cyclic process

First law for a system undergoing change of state

Work and heat transfer for various process for

closed system

PV graph for various processes

Internal energy

Enthalpy

Specific heats for various processes

Solved Examples

5 FIRST LAW APPLIED TO

FLOW PROCESSES

Flow work

Steady flow process

Mass balance

Energy Balance

Steady flow energy equation

Nonflow energy equation

Applications of SFEE

Flow work vs Nonflow work

Variable flow processes

Examples of Variable Flow processes

Solved examples

6 SECOND LAW

OF

THERMODYNAMICS

Limitations of first law

Second law helps….

Thermal energy reservoirs

Directional law for spontaneous process

Difference between heat and work

Cyclic heat engine

Reversed heat engine

Kelvin Planck’s statement

PMM2

Clausius statement

Equivalence of 2 statements

Reversible process

Carnot cycle and reversed Carnot cycle

Carnot theorem

Heat Transportation

Irreversibility

Causes of irreversibility

Types of irreversibility

Solved Examples Clausius Inequality

Concept of Entropy

Entropy in terms of thermodynamic properties

TS diagram for various processes


7 ENTROPY

Entropy Principle

Applications of Entropy Principle

Entropy generation

Solved Example

8 AVAILABLE ENERGY,

AVAILABILITY AND

IRREVERSIBILITY

Available energy

Dead State

Available energy referred to a cycle

Decrease in available energy when heat is

transferred through a finite temperature difference

Available energy from a finite energy source

Quality of energy

Law of degradation of energy

Maximum work in reversible process

Reversible work by an open system exchanging

heat only with the surroundings

Reversible work in steady flow process

Reversible work in a closed system

Useful Work

Maximum work obtainable when system exchanges heat with a thermal reservoir in

addition to atmosphere

Availability

Availability in a steady flow process

Availability in nonflow process

Availability in chemical reaction

Irreversibility and Gouystodola

theorem

Second law efficiency

Solved examples

9

PURE SUBSTANCE

Pure Substance

Phase

Various terms related to study of pure substance

Various property diagram

Dryness fraction

Specific and molar volume

Mass fraction

Mole fraction


10 PROPERTIES

OF GAS MIXTURE

Dalton’s law of partial pressure

Amagatleduc’s law of partial

volumes

11 THERMODYNAMIC

RELATIONS

Maxwell equation

TdS Equation

Heat Capacity Relationship

Energy Equation

Clausius Claypeyron Equation

Internal energy change for an ideal

gas

Enthalpy change

Entropy changes

Joule –Thomson coefficient

SOLVED PROBLEMS


CHAPTER 1

BASIC CONCEPTS IN THERMODYNAMICS

The word THERMODYNAMICS means “Heat in Motion”.

“THERMODYNAMICS is basically a branch of science which focuses on the study of energy

transfer and its effect on various physical properties of the system.”

“THERMODYNAMICS is the study of three E’s i.e. Energy, Entropy and Equilibrium.”

“THERMODYNAMICS is a science that governs following:

Energy and its transformation.

Feasibility of a process involving transformation of energy.

Feasibility of a process involving transfer of energy.

Equilibrium process.

Thus, we can say that THERMODYNAMICS deals with energy conversion, energy exchange

and the direction of exchange.

THERMODYNAMIC SYSTEM

System is that part of universe which is under investigation or under the study of

observer.

Properties of the system are observed when the exchange of energy i.e. work or heat,

takes place.

There is no arbitrary rule for selection of system but proper selection makes the

calculations easy.

SURROUNDINGS

The remaining portion of universe which is external to the system is called as

surrounding.

The exchange of energy takes place between system and surroundings; hence

surroundings may be influenced by the changes taking place in system.


UNIVERSE

System and surroundings together constitutes Universe i.e.

System + Surroundings = Universe.

Figure 1.1

SYSTEM BOUNDARY

System and surroundings in the universe are separated by System boundary.

A system boundary has zero thickness.

Boundary may be Real or Hypothetical and Fixed or Moving.

It is a surface, and since a surface is a two-dimensional object, it has zero volume.

Thus, it attains neither mass nor volume.

Figure 1.2

If heat (energy) exchange doesn’t take place across body it is called adiabatic boundary

otherwise it will be diathermic boundary.


DIFFERENCE BETWEEN SURROUNDINGS, IMMEDIATE SURROUNDINGS AND

ENVIRONMENT

Surroundings are everything outside the system boundaries.

The immediate surroundings refer to the portion of the surroundings that is affected by

the process, and

Environment refers to the region beyond the immediate surroundings whose properties

are not affected by the process at any point.

TYPES OF THERMODYNAMIC SYSTEM

Generally two types of exchange can occur between the system and its surroundings:

Energy exchange (heat or work) and

Exchange of matter (movement of molecules across the boundary of the system and

surroundings).

Based on the type of exchange, it may be classified into three types.

Closed system

Open system

Isolated system

Closed System

Heat and work (energy) crosses the boundary.

No mass transfer takes place i.e. mass of system is fixed, hence it is also called as NON

FLOW SYSTEM.

Due to fixed mass, we also define closed system as CONTROL MASS.

Boundary of the system is not fixed but arbitrarily selected.

Since boundary may change, volume of the system is not necessarily fixed.

Energy transfer can be experienced only at boundaries.

e.g. Piston cylinder arrangement, gas being compressed by a piston in a closed cylinder.

The fluid contained in the cylinder can receive or reject heat, can expand or contract,

hence changing the volume, but no matter (fluid) can flow out or into the cylinder, i.e.

mass remains fixed.


Figure 1.3

Open system

Heat and work crosses the boundary.

Mass transfer also takes place i.e. mass of system is not fixed; hence it is also called as

FLOW SYSTEM.

System boundary is known as CONTROL SURFACE which always remains fixed.

Volume of the system does not change; hence open system is also defined as CONTROL

VOLUME.

e.g. Steam generator or boiler

A steam generator converts water into steam by gaining heat from furnace. Hence water

flows into the system and steam flows out of the system; hence matter is crossing the

boundary of system.

Figure 1.4


Isolated System

Heat and work does NOT cross the boundary.

Mass of the system remains fixed i.e. No mass transfer takes place.

e.g. Thermos flask.

Neither heat flows into/out of the system nor the matter flows.

Thus, a special type of closed system that does not interact with its surroundings is called an

Isolated System.

GATE TIP

Open system

Heat and work crosses the boundary. Mass transfer also takes place i.e. mass of

system is not fixed

Known as FLOW SYSTEM.

Volume of the system does not change.

Closed System

Heat and work (energy) crosses the boundary. No mass transfer takes place.

Known as NON FLOW SYSTEM.

Volume of the system change.

Isolated System

Heat and work does not cross the boundary.. No mass transfer takes place

Classify the following as open, close or isolated system with suitable

reasons:

Cooling system of engine of a car

Pressure cooker

Air compressor


Question on GATE Tip:

Ques 1: A closed thermodynamic system is one in which

(a) There is no energy or mass transfer across the boundary

(b) There is no mass transfer, but energy transfer exists

(c) There is no energy transfer, but mass transfer exists

(d) Both energy and mass transfer take place across the boundary, but the mass transfer is

controlled by valves

Ques 2: Which of the following statements are true?

(a) A closed system is necessarily an isolated system

(b) An isolated system is necessarily a closed system

(c) A system cannot be both closed and isolated.

(d) The concepts of closed and isolated in regards to a system are independent concepts.

Ques 3: Which of these Cases would be best suited for using a control volume approach in the

thermodynamic analysis of the system?

(a) Compression of air in a cylinder

(b) Expansion of gases in a cylinder after combustion

(c) Air in a balloon

(d) Air Filling in a Cycle tyre from any compressor

Solutions

1) (b) As we know that In closed system only energy transfer will happen.

2) Statement (b) is true. Because for isolated system ,system should be a closed system at first.

3) All Systems (a) to (c) are closed systems, so we can’t use control mass for these cases. Only

system (d) is an open system with a fixed boundary because here mass flow and energy transfer

both are taking place so option (d) will be answer.

HOMOGENEOUS AND HETEROGENEOUS SYSTEM

A phase is defined as the quantity of matter which is homogeneous throughout in

chemical composition i.e. chemical composition does not vary within system; and

physical structure i.e. solid, liquid or gas.

The system consisting of single phase is called a homogeneous system. e.g. air, mixture

of water and sugar etc.

The system which consists of more than one phase is called heterogeneous system. e.g.

mixture of water and oil etc.


MACROSCOPIC AND MICROSCOPIC VIEWPOINT

Macroscopic Viewpoint Microscopic Viewpoint

1. A certain quantity of matter is under

investigation without focusing on the

events taking place at molecular level.

2. Properties that define the system can be

measured and can be felt by human

senses.

3. Observations are based on assumption

(properties are average values) since

structure of matter is not considered at

all.

4. The analysis of this approach requires

simple mathematical formula.

1. The behaviour of matter is described by

summing up behaviour of each molecule.

2. Since properties are concerned with

individual molecule, they cannot be felt

by human senses.

3. Exact observations are carried out by

considering the structure of matter.

4. The analysis of approach requires a

large no. of molecules so behaviour of

the molecules is studied by using

advanced statistical and mathematical

methods.

Macroscopic viewpoint is an engineering approach while microscopic viewpoint is a

scientific approach.

PROPERTIES OF SYSTEM

Properties are the descriptive and measurable characteristics of the system.

Properties describe the state of a system i.e. has a definite value when system is in a

particular state.

These are macroscopic in nature and hence, can be measured very easily.

Their differential is exact i.e. value can be determined by simply integrating from one

state to another.

They depend only upon the state of system but not on the path followed by the process,

hence are Point function or State function.


Temperature, pressure, volume energy etc. are the various properties of system.

.

Check for a property:

An expression is a property of the system if its differential is exact.

e.g. Expression is an exact differential of hence is a property. But

alone are not exact differential, hence are not the property of system.

Expression is exact differential if

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INTENSIVE AND EXTENSIVE PROPERTIES

Properties of system may be classified as Intensive or Extensive properties.

INTENSIVE PROPERTIES are those which are independent of mass of system.

Property of small portion of the system defines the property of whole of the system.

Intensive properties are expressed in lower case letters except Pressure (P), temperature

(T).

All the specific properties are intensive properties.

e.g. Pressure (P), temperature (T), density etc.

EXTENSIVE PROPERTIES are mass dependent. Hence their value depends upon the

size of the system.

An extensive property when expressed as per unit mass becomes an intensive property

(Specific property).

Extensive properties are expressed in upper case letter except mass.

e.g. mass (m), energy (E), enthalpy (H), entropy (S) etc.

.

Guru Gyan

Thus, Properties are macroscopic characteristics of a system such

as mass, volume, energy, pressure and temperature etc. to which

numerical values can be assigned at a given time without knowledge

of the past history of the system.


Ques 1: Here two systems S1 and S2 as shown in Figure 2.1.Both the systems are in similar

states. S3 is the combined system of S1 and S2. Is the value of property for S3 same as that for

S1 and S2 or will have some other value?

Guru Gyan:

Intensive properties are those which will be unchanged by any process,

whereas those properties whose values are increased or decreased in

proportion to the enlargement or reduction of the system are called

extensive properties.

If the system consists of mixture of different phases, the phases are

separated from each other by phase boundary. The thermodynamic

properties change abruptly at the phase boundary, even though the

intensive properties like temperature and pressure are identical.


Solution: If property is intensive then S3 will also have same value as S1 and S2 and if property

is extensive then it will not have same value as S1 and S2.

Ques 2: Which of the following are intensive properties?

1. Kinetic energy 2. Specific enthalpy

3. Pressure 4. Entropy

Select the correct answer using the code given below:

(a) 1 and 3

(b) 2 and 3

(c) 1, 3 and 4

(d) 2 and 4

Ans.2 - Specific Enthalpy is defined as enthalpy per unit mass so it will not depend on mass and

Pressure will not depend on mass also. Thus both Specific Enthalpy and Pressure both will be

treated as intensive property.

STATE OF A SYSTEM

State of a system is the condition of system at any point of time.

The state of a simple compressible system can be completely specified by two

independent, intensive properties. (This is also called two property rule or state

postulates)

When one or more than one property of system changes, then a change of state of

system takes place.

Note:

A system is called a simple compressible system in the absence of electrical, magnetic,

gravitational, motion, and surface tension effects. (These effects are nearly negligible in

the most of the engineering problems )

Two properties are independent if one property can be varied while the other one is held

constant.

Temperature and specific volume, for example, are always independent properties, and

together they can fix the state of a simple compressible system


THERMODYNAMIC PROCESS, PATH AND CYCLE

Any change that a system undergoes from one equilibrium state to another is called a

process

The series of states through which a system passes during a process is called the path of

the process

Figure 1.6

When change of state takes place in such a way that the initial and final states of system

are identical, then the process is called thermodynamic cycle.

Figure 1.7

Dialogue box…..

I.C. Engine does not execute thermodynamic cycle. Explain.

Dialogue box….

Temperature and pressure, however, are independent properties for single-phase systems,

but are dependent properties for multiphase systems. Explain.


THERMODYNAMIC EQUILIBRIUM

A system is said to be in thermodynamic equilibrium if the conditions are satisfied for:

Mechanical equilibrium

Chemical equilibrium

Thermal equilibrium

Phase equilibrium

Mechanical equilibrium in system exists when there is no change in pressure at any point of

system with time i.e. uniformity of pressure. It also means that there is no any unbalanced force.

In other words, there is no pressure gradient within the system.

The variation of pressure as a result of gravity in most thermodynamic

systems is relatively small and usually disregarded.

Still water contained in a tank is also considered to be in mechanical

equilibrium, though the pressure increases as one move downward from

free water surface.

Chemical equilibrium in a system exists when there is no change in chemical

composition with time i.e. no chemical reaction takes place.

Thermal equilibrium in a system exists when there is no temperature differential within

system.

Temperature is same throughout the entire system.

Fluids comprising the system are not chemically reactive since it may raise

temperature of system by chemical reaction.

Phase equilibrium in a multiphase system exists when the mass of each phase reaches an

equilibrium level and stays there.

Note:

A system is said to be in non-equilibrium state if any one of the above condition is

not satisfied by the system.

In non-equilibrium, states passed by the system cannot be described by

thermodynamic properties which represent the system as a whole.

When a system remains in equilibrium state, it should not undergo any changes on its own.

QUASI-STATIC PROCESS

When a process proceeds in such a manner that the system remains infinitesimally close

to an equilibrium state at all times, it is called a quasi-static, or quasi-equilibrium,

process.


Thus, clear state properties (pressure, temperature etc.) can be assigned to the system at

every moment. A quasi-static process can thus be represented by a set of continuous

points on a state-space diagram (e.g., a p − V diagram or a T − v diagram).

Features of Quasi-Static Process

A quasi-equilibrium process is a sufficiently slow process that allows the system to adjust

itself internally so that properties in one part of the system do not change any faster than

those at other parts.

Frictionless quasi-static processes are reversible.

These are idealized process and not the true representation of actual process.

Every state passed may be regarded as equilibrium state.

Infinite slow process and easy to analyze.

All work producing devices work on this principle.

Guru Gyan:

A process is said to be reversible if the system and its surroundings

are restored to their respective initial states by reversing the direction of the process. A reversible process has to be quasi-static,

but a quasi – static process is not necessarily quasi-static.


Examples:

Quasi-static: Slow expansion of a piston and cylinder system such that pressure and volume can

be clearly defined at every point in time.

Non quasi-static: Sudden expansion of the piston-cylinder system. Pressure in the system cannot

be specified at every point in time.

Quasi-static: Two bodies exchanging energy in the form of heat such that the temperature of

each body is clearly defined at every point of time.

Non quasi-static: Rapid removal of energy from one surface of a reasonably large system such

that there is no unique temperature for the system.

Reversible Process

A process in which an infinitesimal change in the driving potential can reverse the direction of

the process.

Example: A piston expanding against an external pressure. The driving potential is the pressure

difference which is infinitesimal. At any stage, if the external pressure is increased

infinitesimally, the piston should start moving the opposite way.

Or Else: Heat transfer occurring due to a temperature difference between two bodies. The

temperature difference between the two bodies is infinitesimal. If the temperature of body

receiving energy is changed infinitesimally, the direction of heat transfer also changes.

NOTE: A reversible process is necessarily quasi-static though the opposite is not true. For

example, consider heat exchange between a really well insulated vessel at temperature T1 and

the surroundings which are at T2 far lesser than T1. Changing either T1 or T2 does not reverse

the direction of the process, though it is slow enough to be quasi-static.

Ques 3: Which Of The Following Is/Are Reversible Process(es)?

1. Isentropic expansion

2. Slow heating of water from a hot source

3. Constant pressure heating of an ideal gas from a constant temperature source

4. Evaporation of a liquid at constant temperature

Select the correct answer using the code given below:

(a) 1 Only

(b) 1 And 2

(c) 2 And 3

(d) 1 And 4


Solution:

(d) Isentropic expansion and evaporation of a liquid at constant temperature. Isentropic

expansion is also known as reversible adiabatic process (which will be discussed in later

chapter).

CONCEPT OF CONTINUUM

Despite the large gaps between molecules, a substance can be treated as a continuum

because of the very large number of molecules even in an extremely small volume.

It assumes a continuous distribution of mass within the matter or system with no

empty space, instead of the actual conglomeration of separate molecules.

If the mean free path is very small as compared with some characteristic length in the

flow domain (i.e., the molecular density is very high) then the gas can be treated as a

continuous medium. If the mean free path is large in comparison to some characteristic

length, the gas cannot be considered continuous.

The continuum idealization allows us

to treat properties as point functions and

to assume the properties vary continually in space with no jump

discontinuities.

This idealization is valid as long as the size of the system we deal with is large relative to

the space between the molecules.

PATH FUNCTION AND POINT FUNCTION

Point Functions

They depend only upon the initial and final condition (state) of the system but not on the

path followed by the system.

They have exact differential i.e. their integration can be carried out simply.

Differential amount is represented by symbol “d” i.e. small change in volume will be

expressed as dV.

Change in value can be expressed as the difference between initial and final value.

Thermodynamic properties are point functions since for a given state there is a definite

value for each property and is independent of the path the system follows during the

change of state.


In a cycle, since initial and final states are identical, the cyclic integral of a property

(point function) is always zero i.e. .

Path Functions

They depend upon the path followed by the system.

They have inexact differential.

Differential amount is represented by symbol i.e. for small work done and small

heat transfer

Work and heat are the path functions.

Change in the value can NOT be expressed as the difference between initial and final

value.

W1-2 (but not W)

Before integration, multiplication with integrating factor is required.

WORKING SUBSTANCE

A working substance refers to a fluid in thermodynamic devices to serve as a medium for

transport of energy between the system and surroundings.

Fluid may be gas, vapour, liquid or any nonreactive mixture of these constituents.

Working substance may change their phase during processes occurring in the system.

Example – refrigerants used in refrigeration and air-conditioners, water vapour used in

steam power plants.


GATE Tip

Intensive Property

Independent of mass

Extensive Property

mass dependent.

value depends upon the size of the system.

Specific property

An extensive property when expressed as per unit mass becomes an intensive

property.

Point Functions

They depend only upon the initial and final condition

not on the path followed by the system.

exact differential

Cyclic integral of a property (point function) is always zero

Path Functions

Depend upon the path followed by the system.

Inexact differential.

PRESSURE

Pressure is defined as a normal force exerted by a fluid per unit area

SI unit of Newton per square meter (N/m2), which is called a Pascal (Pa). That is,

Atmospheric pressure is measured by a device called a barometer; thus, the

atmospheric pressure is often referred to as the barometric pressure.


The actual pressure at a given position is called the absolute pressure, and it is measured

relative to absolute vacuum (i.e., absolute zero pressure).

Pressures below atmospheric pressure are called vacuum pressures and are measured by

vacuum gages that indicate the difference between the atmospheric pressure and the

absolute pressure.

Pressure in a fluid at rest is independent of the shape or cross section of the container. It

changes with the vertical distance, but remains constant in other directions. Therefore, the

pressure is the same at all points on a horizontal plane in a given fluid.

A consequence of the pressure in a fluid remaining constant in the horizontal direction is

that the pressure applied to a confined fluid increases the pressure throughout by the

same amount. This is called Pascal’s law.

Hydrostatic law defines the variation of pressure in a fluid with height as .

The pressure gauges used in engineering applications measure Absolute pressure.

Figure 1.9


Ques 1: Convert the following readings of pressure to kPa, assuming that the barometer reads

760 mmHg:

(a) 80 cm Hg gauge (b) 50 cm Hg vacuum

(c) 1.2 m H2O gauge (d) 5.3 bar

SOLUTION:

760 mm Hg = 0.760 × 13600 × 9.81 Pa

= 10139.16 Pa

≈ 101.4 kPa

(a) 80 cm Hg gauge

= 0.80 × 13600 × 9.81 × 10-3

+ 101.4 kPa

= 106.732+ 101.4 kPa

= 208.132kPa

(b) 50 cm Hg vacuum

= (76 – 50) cm (absolute)

= 0.26 × 13.600 × 9.81 kPa

= 34.68 kPa

(c) 1.2 m H2O gauge

= 1.2 × 1000 × 9.81 × 10-3

+ 101.4 kPa

= 113.172 kPa

(d) 5.3 bar = 5.3 × 105Pa = 530 kPa

Ques 2: Any vertical column having height of 60m and fluid in vertical column having density

1878 kg/m3 exists in a place where g = 9.65 m/s2. What is the pressure at the base of the

column?

Solution: Pressure at depth p = z ρg

= 60 × 1878 × 9.65

= 1087.62 Pa


MASS DENSITY

The amount of working substance contained in a given volume is called as mass density

of that substance.

Kg/m

3

Ques 3: A pump discharges a liquid into a drum having 3 m in diameter and 8.40 m in length,

can hold 3000 kg of the liquid. Find the density of the liquid?

Solution:

Volume of drum = π/4 ×d2x h

= (π 32 x8.4) /4

= 59.376 m3

Density=

=

WEIGHT DENSITY (SPECIFIC WEIGHT)

Weight per unit volume is called as specific weight.

ϓs

ρg N/m

3

Specific weight of a substance may vary with location on earth.

SPECIFIC VOLUME

Volume per unit mass is called specific volume.

m

3/Kg

It is the reciprocal of mass density.

SPECIFIC GRAVITY

It is the ratio of the density of a fluid to the density of a standard fluid at a specified

temperature.

For liquids, standard fluid is water at 40C for which ρH2O =1000kg/m

3.

SG =

ρ


For gases, air or hydrogen at 00C is taken as standard fluid.

Specific gravity is a dimensionless quantity.

Specific gravity of mercury is 13.6. This means that mercury is13.6 times heavier than

water.

STANDARD TEMPERATURE AND PRESSURE

At STP, the temperature is taken as 150C and pressure is taken as 1.01325 bar

(atmospheric pressure)

NORMAL TEMPERATURE AND PRESSURE

At NTP, the temperature is taken as 00C and pressure is taken as 1.01325 bar

(atmospheric pressure)


OTHER SOLVED EXAMPLES

Ques 1.

A large chamber is separated into two compartments which are maintained at different pressures.

Pressure gauge A reads 180 kPa, and pressure gauge B reads 120 kPa. If barometric pressure is

100 kPa, determine the absolute pressure existing in the compartments and the reading of gauge

C.

Figure 1.10

Approach: Pressure gauge A has been installed on the wall where pressure due to gases in x and

y are acting in opposite direction, hence it will read a pressure difference of both.

Similarly, Pressure gauges B and C reads the pressure difference between respective chamber

and atmosphere.

SOLUTION:

Let x kPa and y kPa be absolute pressures in compartments X and Y respectively.

B

C X Y

A


Ques 2.

The pressure and specific volume of the atmosphere are related according to equation

, where p is in N/m2 and v in m

3/kg. What depth of atmosphere is required to produce a

pressure of 1.033 bar at the earth surface? Assume g=9.81 m/s2.

Approach: Earth surface is surrounded by a fluid i.e. air. The pressure inside the fluid varies

vertically. Hence there exists a pressure difference between pressure at top of air column and at

earth surface. This pressure difference can be used to obtain the height of air column using

hydrostatic law i.e.

SOLUTION:

Let H be the depth of atmosphere required to produce a pressure of 1.033 bar and A be the area

of air column. Consider an element dh of this height. Let p be pressure acting above and p+dp

be acting below the element.

Force balance:

Solving the equation,

Integrating,

Hence, atmospheric pressure exists on earth surface due to the air column lying above the

earth surface.

Ques 3: In a condenser Vacuum Gauge reads around 0.72 mHg. Calculate absolute pressure in

the condenser in kPa (where the atmospheric pressure = 101.3 kPa)?

Solution:

Absolute pressure = atmospheric pressure – vacuum pressure

= 101.3 – 0.66 × 13600 × 9.81 × 10-3

kPa

= 101.3- 96.059 kPa

=5.24 kPa


PRACTICE SET

1. Which of the following is correct?

a. Absolute pressure = Gauge pressure + Atmospheric pressure

b. Gauge pressure = Absolute pressure + Atmospheric pressure

c. Atmospheric pressure = Absolute pressure + Gauge pressure

d. Absolute pressure = Gauge pressure × Atmospheric pressure

2. Which of the following is an example of closed system?

a. Thermosflask

b. Pressure cooker

c. Steam turbine

d. All of above

3. Which of the following expressions are true?

a. 1, 2

b. 1

c. 2

d. 2, 3

4. A diathermic wall allows flow of

a. Heat and matter

b. Only heat

c. Only matter

d. None of these

5. Atm is…..

a. 1.01325 Mpa

b. 1.0 Mpa

c. 1.005 Mpa

d. 760 Kpa


6. The Barometer reading 760 mm hg equals

a. 90 cm hg Gauge

b. 40 cm hg Vacuum

c. 10.336 m H2o Gauge

d. 3.1 Bar

7. A 30 m high vertical column of a fluid of density 1878 kg/m3 exists in a place where g =

9.65 m/s2. What is the pressure at the base of the column?

a. 501.45 Kpa

b. 600.25 Kpa

c. 644.67 Kpa

d. 543.68 Kpa

Answers and Hints:

1-a 2-b 3-c 4-b 5-a 6-c 7- hint (p = ρgh)


GATE QUESTIONS:

Question1: The pressure gauges G1 and G2 installed on the system show pressures of PG1 = 5.00

bar and PG2 = 1.00 bar. Value of unknown pressure P is

(A) 1.01 bar (B) 2.01 bar

(C) 5.00 bar (D) 7.01 bar

Solution:

P = 2GP + Atmospheric pressure

= 1.00 + 1.0

= 2.01 bar.

THERMODYNAMICS...Steady flow process Mass balance Energy Balance Steady flow energy equation Nonflow...

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